Nuclear stability and variations of SM params

My question is, how sensitive is it to the variation of SM parameters?
Imagine that I am sitting in front of some magic TV, where the image above is displayed. Below there are sliders, one per SM parameter. I start to move these sliders, looking at the screen.

So how sensitive is function of nuclear stability to the small variation of parameters, how much do I need to change to start seeing any difference or to completely change they way how it looks?

Of course there are no exact answers, but any rough estimations - like 1%, 0.01%, or 0.00000001%?

Staff: Mentor

You can extract the general shape of that diagram with the mass formula. The coefficients depend on fundamental parameters - not strictly linear, but at least something similar.

If you increase the fine-structure constant by 1%, the coulomb term will increase by 2%, and large nuclei need a few neutrons more to be stable (similar to 2%, I would guess, which corresponds to ~3-5 neutrons).

If you increase the strong force by 1%, volume and surface term will change in a similar way, and I would expect that more (heavier) nuclei become stable or long-living.

If you change the up- or down-quark masses, the ratio protons/neutrons will change a bit.

If you change the strength of the weak interaction or the W boson mass, you change the half-life of beta decays. That influence is certainly nonlinear.

Other constants: Hmm...

Cosmology can be more sensitive to some changes - if neutrons would be >0.5 MeV lighter than protons for example, protons would decay to stable neutrons, and stars (if they would exist at all) would look completely different. The Triple-alpha_process is quite sensitive to energy states, too.